Simple Semi-analytical Model Research Articles

A New Method To Predict Performance of Horizontal and Multilateral Wells

Summary Production enhancement and ultimate recovery improvement have given horizontal wells the edge over vertical wells in many marginal reservoirs. However, it is more expensive to drill and complete a horizontal well than a vertical one. Therefore, to determine the economical feasibility of drilling a horizontal well, engineers need reliable methods to estimate its productivity. After a broad literature review, a simple semianalytical model has been developed in this study for predicting the productivity of horizontal oil wells. This model couples flow from a box-shaped drainage volume to flow in the wellbore. Along with friction, acceleration, and fluid-inflow effect, change in flow regime from laminar to turbulent is also taken into account to describe flow in the wellbore. The reservoir-inflow model used in this productivity model represents flow in the reservoir using a combination of 1D and 2D models and also considers varying skin along the wellbore to account for the heterogeneity of the near-wellbore region because of drilling-fluid invasion into the formation. In addition, reservoir-permeability anisotropy and convergence of flow to the wellbore have been taken into account in this inflow model. Comparison of this model with three existing models using field data reveals that the proposed model is more accurate because of more-realistic modeling of reservoir inflow and wellbore flow. The semianalytical nature of this coupling model makes it comprehensive and applicable to reservoirs with varying conditions, especially heterogeneous reservoirs. Moreover, this productivity model can be extended easily to estimate the deliverability of multilateral wells by coupling the inflow performance of individual laterals with hydraulics in buildup sections and the main vertical section. A logical procedure for calculating the deliverability of multilateral wells by using this productivity model is described in this paper.

Application of recent results on the orbital migration of low mass planets: convergence zones

AbstractPrevious models of the combined growth and migration of protoplanets needed large ad hoc reduction factors for the type I migration rate as found in the isothermal approximation. In order to eliminate these factors, a simple semi-analytical model is presented that incorporates recent results on the migration of low mass planets in non-isothermal disks. It allows for outward migration. The model is used to conduct planetary populations synthesis calculations. Two points with zero torque are found in the disks. Planets migrate both in- and outward towards these convergence zones. They could be important for accelerating planetary growth by concentrating matter in one point. We also find that the updated type I migration models allow the formation of both close-in low mass planets, but also of giant planets at large semimajor axes. The problem of too rapid migration is significantly mitigated.

Determination of modal effective indices and dispersion of microstructured fibers with different configurations: a variational approach

A simple semi-analytical model based on the variational method is developed for determining the effective indices of the fundamental modes and consecutively the dispersion properties of microstructured optical fibers (MOFs) with different lattice geometries without resorting to any numerical tool. We consider an equivalent step-index (ESI) profile of the MOF and the fundamental mode shape is approximated as a simple Gaussian function in the core. Effective index data and dispersion obtained from the proposed variational method offer reasonable agreement with numerically derived data using the Finite Element Method (FEM). The proposed model offers an alternative and swift way for reasonably precise determination of the effective index of the fundamental mode and dispersion properties of MOF designs with different lattice geometries. Finally, as a major application, the dispersion property of a fabricated MOF, derived through the proposed variational method, is directly used in order to model experimental supercontinuum (SC) spectra with satisfactory agreement.

Numerical inversion and analysis of tephra fallout deposits from the 472 AD sub-Plinian eruption at Vesuvius (Italy) through a new best-fit procedure

A simple semi-analytical model for ash-fall deposit was applied to reconstruct the tephra deposits of the sub-Plinian 472 AD eruption of Vesuvius, Italy, which is of the scale of the reference eruptive scenario for the emergency planning, at Vesuvius. Applying a novel least-squares method, the bulk grain-size distribution, the total mass, and the eruption column height were obtained by fitting the computed ground load and granulometries with the observed ones. The analysis of the effect of three different weighting factors in the minimization procedure was also performed. Results showed that the statistical weighting factor produced the minimum bias. The best correlation between calculated and measured deposit was found, even though the quantity of the input data was not very high, as it commonly occurs for several ancient eruptions. Model results were also in agreement with estimations provided by other independent methods.

Tunnel coupling in an ensemble of vertically aligned quantum dots at room temperature

We report unambiguous observation of the formation of mixed electronic states in an ensemble of self-assembled vertically aligned quantum dots at room temperature. Three closely spaced layers containing stacked In(Ga)As/GaAs quantum dots are placed in the active region of a two-section semiconductor device, and investigations of the quantum-dot optical properties at different applied electric fields are carried out by means of differential-absorption spectroscopy. A simple semianalytical model, which describes absorption of two layers of coupled quantum dots with an account of the size dispersion, is developed. A comparison between our experimental and theoretical results allows clear attribution of the observed low-photon-energy field-dependent spectral features to the four mixed optical transitions due to the two upper quantum-dot layers. Interpretation of the experimental results reveals an anticrossing of spatially direct and indirect transitions characterized by the energy splitting of approximately 30 meV.

Experimental and theoretical study of absorption of femtosecond laser pulses in interaction with solid copper targets

The reflectivity of near-infrared 150 fs laser pulses from copper targets has been measured in the intensity range of $6\ifmmode\times\else\texttimes\fi{}{10}^{11}\char21{}1.6\ifmmode\times\else\texttimes\fi{}{10}^{14}\text{ }\text{W}\text{ }{\text{cm}}^{\ensuremath{-}2}$, showing a drop in reflectivity versus intensity as the target is heated. A simple semianalytical model of femtosecond electron heating and resultant optical absorption is developed to describe the time dependent and integral reflectivity covering the range from cold metal response to hot plasma response. The model is in good agreement with experimental ultrafast reflectivity measurements over the intensity range studied.

On the width and shape of the corotation region for low-mass planets

We study the coorbital flow for embedded, low mass planets. We provide a simple semi-analytic model for the corotation region, which is subsequently compared to high resolution numerical simulations. The model is used to derive an expression for the half-width of the horseshoe region, x_s, which in the limit of zero softening is given by x_s/r_p = 1.68(q/h)^(1/2), where q is the planet to central star mass ratio, h is the disc aspect ratio and r_p the orbital radius. This is in very good agreement with the same quantity measured from simulations. This result is used to show that horseshoe drag is about an order of magnitude larger than the linear corotation torque in the zero softening limit. Thus the horseshoe drag, the sign of which depends on the gradient of specific vorticity, is important for estimates of the total torque acting on the planet. We further show that phenomena, such as the Lindblad wakes, with a radial separation from corotation of ~ a pressure scale height H can affect x_s, even though for low-mass planets x_s << H. The effect is to distort streamlines and to reduce x_s through the action of a back pressure. This effect is reduced for smaller gravitational softening parameters and planets of higher mass, for which x_s becomes comparable to H.

Star formation in the multiverse

We develop a simple semianalytic model of the star formation rate as a function of time. We estimate the star formation rate for a wide range of values of the cosmological constant, spatial curvature, and primordial density contrast. Our model can predict such parameters in the multiverse, if the underlying theory landscape and the cosmological measure are known.

Reversible separation of single-walled carbon nanotubes in bundles

We show that electrostatic charging of nanotubes and the consequent repulsion can lead to reversible separation of individual single-walled carbon nanotubes in bundles. Low-energy electron beam irradiation leads to this completely reversible phenomenon. A simple semianalytical model is used to explain the observed separation mechanism. The reversibility of the separation process is attributed to discharging and thermal-fluctuation induced motion of the nanotubes in ambient air. Further, the separation impacts the electrical conductance of small nanotube bundled devices.

A simple semi-analytical model for remote estimation of chlorophyll- a in turbid waters: Validation

Accurate assessment of phytoplankton chlorophyll- a (chl a) concentrations in turbid waters by means of remote sensing is challenging due to the optical complexity of case 2 waters. We have applied a recently developed model of the form [ R rs − 1 ( λ 1) − R rs − 1 ( λ 2)] × R rs( λ 3) where R rs( λ i ) is the remote-sensing reflectance at the wavelength λ i , for the estimation of chl a concentrations in turbid waters. The objectives of this paper are (a) to validate the three-band model as well as its special case, the two-band model R rs − 1 ( λ 1) × R rs( λ 3), using datasets collected over a considerable range of optical properties, trophic status, and geographical locations in turbid lakes, reservoirs, estuaries, and coastal waters, and (b) to evaluate the extent to which the three-band model could be applied to the Medium Resolution Imaging Spectrometer (MERIS) and two-band model could be applied to the Moderate Resolution Imaging Spectroradiometer (MODIS) to estimate chl a in turbid waters. The three-band model was calibrated and validated using three MERIS spectral bands (660–670 nm, 703.75–713.75 nm, and 750−757.5 nm), and the 2-band model was tested using two MODIS spectral bands ( λ 1 = 662–672, λ 3 = 743–753 nm). We assessed the accuracy of chl a prediction in four independent datasets without re-parameterization (adjustment of the coefficients) after initial calibration elsewhere. Although the validation data set contained widely variable chl a (1.2 to 236 mg m − 3 ), Secchi disk depth (0.18 to 4.1 m), and turbidity (1.3 to 78 NTU), chl a predicted by the three-band algorithm was strongly correlated with observed chl a ( r 2 > 0.96), with a precision of 32% and average bias across data sets of − 4.9% to 11%. Chl a predicted by the two-band algorithm was also closely correlated with observed chl a ( r 2 > 0.92); however, the precision declined to 57%, and average bias across the data sets was 18% to 50.3%. These findings imply that, provided that an atmospheric correction scheme for the red and NIR bands is available, the extensive database of MERIS and MODIS imagery could be used for quantitative monitoring of chl a in turbid waters.

Simple Model for Analyzing Transient Pumping from Two Aquifers with Cross Flow

A simple semianalytical model is proposed for calculating the drawdown due to pumping a well tapping two aquifers. The new model can take into account the transient pumping discharge and cross flow between the aquifers. The transient contributions of the aquifers to the pumped discharge can also be implicitly obtained using the model.

Simple Model for Analyzing Transient Pumping from Two Aquifers without Cross Flow

A simple semianalytical model is proposed for calculating the drawdown due to pumping a well tapping two aquifers. The new model can take into account the transient pumping discharge and cross flow between the aquifers. The transient contributions of the aquifers to the pumped discharge can also be implicitly obtained using the model.

Nonuniform Mobility-Enhancement Techniques and Their Impact on Device Performance

Nowadays, process-induced stress is the preferential industrial method to enhance circuit performances. One of the most popular techniques is the strain induced by contact etch-stop layer. This technology induces a drain-current enhancement which depends on the device dimensions. This strong behavior has already been reported in the literature. In this paper, we propose a simple semianalytical physical model to understand the origin of this dependence and to highlight the physical limitations of the stress techniques. With this model, after a calibration, it would be possible to predict the MOSFET performance for a given transistor gate length. This approach is validated by experimental data and explains the reduction of the drain-current enhancement that is observed for ultrasmall gate-length MOSFET.

Relationship between the attenuation of downwelling irradiance at 490 nm with the attenuation of PAR (400 nm–700 nm) in the Baltic Sea

The vertical attenuation coefficient of diffuse downwelling irradiance at 490 nm ( K d 490) is a parameter that we routinely derive from SeaWiFS images of the Baltic Sea. Here, through model simulations, we examine the relationship between K d(490), and the vertical attenuation coefficient of PAR ( K d PAR), as this later coefficient determines the light available for aquatic photosynthesis. A simple semi-analytical model is used to predict K d(490) and K d(PAR), as a function of the concentrations of chlorophyll, colored dissolved organic material (CDOM), suspended inorganic, and suspended organic particulate material. A series of model simulations based on variations in these optically significant constituents over a range realistic for the Baltic Sea, are used to define the relationship between the two attenuation coefficients. K d ( PAR ) = 0.6677 K d ( 490 ) 0.6763 . This relationship was verified, using data collected independently from the data set used to derive model coefficients, and appears robust when applied to the Baltic Sea. Comparison to other studies and model sensitivity analyses suggest that the relationship will be dependent on relatively large regional variations in CDOM absorption. A relationship between K d(490) and Secchi disk depth was also developed and verified. This relationship while useful was more uncertain. The uncertainty was related to a greater influence of scattering on Secchi disk depth estimates and the corresponding parameterization of scattering in our model.

Galactic dynamos supported by magnetic helicity fluxes

We present a simple semi-analytical model of non-linear, mean field galactic dynamos and use it to study the effects of various magnetic helicity fluxes. The dynamo equations are reduced using the 'no-z' approximation to a non-linear system of ordinary differential equations in time; we demonstrate that the model reproduces accurately earlier results, including those where non-linear behaviour is driven by a magnetic helicity flux. We discuss the implications and interplay of two types of magnetic helicity flux, one produced by advection (e.g. due to the galactic fountain or wind) and the other, arising from anisotropy of turbulence as suggested by Vishniac & Cho. We argue that the latter is significant if the galactic differential rotation is strong enough: in our model, for R ω ≤ -10 in terms of the corresponding turbulent magnetic Reynolds number. We confirm that the intensity of gas outflow from the galactic disc optimal for the dynamo action is close to that expected for normal spiral galaxies. The steady-state strength of the large-scale magnetic field supported by the helicity advection is still weaker than that corresponding to equipartition with the turbulent energy. However, the Vishniac-Cho helicity flux can boost magnetic field further to achieve energy equipartition with turbulence. For stronger outflows that may occur in starburst galaxies, the Vishniac-Cho flux can be essential for the dynamo action. However, this mechanism requires a large-scale magnetic field of at least ≃1 μG to be launched, so that it has to be preceded by a conventional dynamo assisted by the advection of magnetic helicity by the fountain or wind.

Modelling active galactic nuclei: ongoing problems for the faint-end of the luminosity function

We consider simple semi-analytic models that relate the active galactic nuclei (AGNs) evolution to the merging history of their host dark matter haloes and quantify their ability of matching the AGN luminosity function (LF) and its spatial clustering at low and intermediate redshifts. In particular, we focus on the recent determinations of the AGN LF in the hard X-ray band at z∼ 0 which constitutes the most stringent observational test for our models. Indeed, while we find an acceptable agreement between the model bolometric LF and the data at 1 ≲z≤ 2 and for luminosities larger then 1010 L bol,⊙, no semi-analytic model is capable of reproducing the number density of faint X-ray sources in the local universe. Some improvement can be obtained by advocating energy feedback that we model through a time-dependent Eddington ratio. Even in this case, however, the number density of faint AGNs is significantly below observations. This failure indicates that major mergers cannot constitute the only trigger to accretion episodes in the local AGN population.

Ultra-high energy cosmic ray investigations by means of EAS muon density measurements

A new approach to investigations of ultra-high energy cosmic rays based on the ground-level measurements of the spectra of local density of EAS muons at various zenith angles is considered. Basic features of the local muon density phenomenology are illustrated using a simple semi-analytical model. It is shown that muon density spectra are sensitive to the spectrum slope, primary composition, and to the features of hadronic interaction. New experimental data on muon bundles at zenith angles from 30° to horizon obtained with the coordinate detector DECOR are compared with CORSIKA-based simulations. It is found that measurements of muon density spectra in inclined EAS give possibility to study characteristics of primary cosmic ray flux in a very wide energy range from 10 15 to 10 19 eV.

Propagation Delay of an &lt;emphasis&gt;RC&lt;/emphasis&gt;-Chain With a Ramp Input

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this brief, two simple semi-analytical models which allow the estimation of the propagation delay of an <emphasis>RC</emphasis>-chain with a linear input are presented. The closed-form models can be used to evaluate the propagation delay of wires in modern VLSI and ULSI processes. The two approximations, a continuous function and a piecewise function, exhibit a maximum error lower than 15% at the end of the chain. The models have been validated extensively through circuit simulations. In particular, 1000 different <emphasis>RC</emphasis>-chains have been considered and simulated demonstrating the accuracy of the proposed models with respect to the most widely used Elmore delay metric. </para>

A semi-analytical solution for random wave-induced soil response and seabed liquefaction in marine sediments

In this study, unlike most previous investigations for wave-induced soil response, a simple semi-analytical model for the random wave-induced soil response is established for an unsaturated seabed of finite thickness. Two different wave spectra, the B-M and JONSWAP spectra, are considered in the new model. The influence of random wave loading on the soil response is investigated by comparing with the corresponding representative regular wave results through a parametric study, which includes the effect of the degree of saturation, soil permeability, wave height, wave period and seabed thickness. The maximum liquefaction depth under the random waves is also examined. The difference on the soil response under the two random wave types, B-M and JONSWAP frequency spectra, is also discussed in the present work.

High power 4H–SiC pin diodes (10 kV class) with record high carrier lifetime

The hole lifetime τp in the n-base and isothermal (pulse) current–voltage characteristics have been measured in 4H–SiC diodes with a 10kV blocking voltage (100μm base width). The τp value found from open circuit voltage decay (OCVD) measurements is 3.7μs at room temperature. To the best of the authors’ knowledge, the above value of τp is the highest reported for 4H–SiC. The forward voltage drops VF are 3.44V at current density j=100A/cm2 and 5.45V at j=1000A/cm2. A very deep modulation of the blocking base by injected non-equilibrium carriers has been demonstrated. Calculations in term of a simple semi-analytical model describe well the experimental results obtained.